silverflamein wrote:What is the standard deviation of a given set of numbers whose avg is 5?
1) none of the numbers are greater than their avg.

2) the standard deviation is 5 when the values of each of the given numbers is increased by 7.

neelgandham's solution is perfect.

However, for the record, this could never be an official GMAT question, since the two statements contradict each other. On the GMAT, the statements will never contradict each other. In fact, you can use this fact to help identify errors in your calculations (see video #10 at: https://www.gmatprepnow.com/module/gmat-data-sufficiency - it's free)

Statement 1: if none of the numbers are greater than the avg, then all of the numbers must be 5.
This means the SD is 0

Statement 2: As neelgandham pointed out, this statement tells us that the SD is 5

Since the SD cannot equal both 0 and 5, we have a contradiction.

Cheers,
Brent